DOC《第三章 效用论》

四、计算题 1.max:U=2X2Y S.T 360=3X+2Y 构造拉格朗日函数得:W=2X2Y+λ(360-3X-2Y) dW/Dx=MUx-3λ=4xy-3λ=0 dW/Dy=MUy-2λ=2x2-2λ=0 求得:4Y=3X,又360=3X+2Y,得X=80,Y=60 2.PXX + PYY = M 2X + Y =

20 U = X3(20-2X)2 = 400X3 ― 80X4 + 4X5 效用极大 1200X2 -320X3 + 20X4 =

0 解得X1 =

0 ,X2 =

6 ,X3 =

10 X = 0或10时U =

0 ,不合题意 所以X =

6 ,Y =

8 . ........